| In the development of the Internet era,multi-agent systems have been widely studied.Positive system is a special kind of dynamical system;it has been extensively used in many fields.Inputto-state stability theory plays a vital status in the development of modern nonlinear control theory,especially in the robust stability theory of nonlinear systems.In practice,disturbances for multiagent systems are common,but there is no consistency study on positive multi-agent systems with disturbances.In this thesis,the input-to-state consistency of nonlinear positive multi-agent systems under state feedback and implusive control is studied.The main research work is as follows:In this thesis,the input-state stability and stabilization of nonlinear impulsive positive systems are studied by using the maximum separable Input-state stability Lyapunov function.Firstly,sufficient conditions for input-state stability of general nonlinear impulsive systems are proposed.On that basis,the criteria of input-state stability for linear and affine nonlinear impulsive positive systems are given.Through them,the properties of input-state stability can be directly judged from the algebraic and differential characteristics of the systems.Then,utilizing the inputstate stability criteria,state-feedback and impulsive controllers are designed for linear and affine nonlinear impulsive positive systems,respectively,which make the systems input-to-state stabilizable.Lastly,three numerical examples are given to verify the effectiveness of our results.Based on the above theory,input-state consistency of nonlinear positive multi-agent systems is studied in this thesis.Firstly,sufficient conditions for the input-to-state consensus of nonlinear positive multi-agent systems under state feedback and impulsive control are given by using the max-separable input-to-state stability Lyapunov function method.Then,sufficient conditions for the input-to-state consensus of the multi-agent systems under state feedback and impulse control are obtained for nonlinear positive multi-agent systems with non-zero positive equilibrium points.Finally,the validity of the results is verified by four numerical examples. |
